1. Field of the Invention
The present invention relates to a method of synchronizing two nodes of a communications network in time and frequency. More specifically, frequency and time are synchronized independently to improve stability and reduce cost in a satellite communication system.
2. Background of the Related Art
In the related art, satellite networks with “star” connectivity are used in various applications. For example, a hub of the star network transmits an outbound continuous time signal. The outbound signal is usually Time Division Multiplexed (TDM), and contains packets for a particular terminal or alternatively, multicast data. Correspondingly, the return link from the terminals to the hub uses Time Division Multiple Access (TDMA). In the related art, standardization of the TDMA return link has been attempted with the outbound signal using the Digital Video Broadcast (DVB) format, as discussed in Digital Video Broadcasting (DVB); Interaction channel for Satellite Distribution Systems; DVB-RCS001rev14, Apr. 3, 2000 (hereafter referred to as “Reference 1”).
The related art scheme for synchronizing the terminals to the hub in time and frequency suggested in Reference 1 uses a timestamp generated at the hub known as a Program Clock Reference (PCR), alternatively referred to as a Network Clock Reference (NCR). The PCR timestamps are transmitted by the hub periodically (e.g., once every 100 milliseconds) in the TDM stream, and are received by all the terminals. The terminals use the PCR to adjust their local oscillators. Thus, the terminals are synchronized in frequency and time with the hub.
In the aforementioned related art system, the PCR is set to the value of a counter driven by a stable source (e.g., GPS based) at the hub. The counter at the hub is sampled just before the PCR transmission on the TDM stream. Additionally, another counter (referred to as the Local Master Counter (LMC)) is maintained at each of the terminals, and is driven by a temperature controlled crystal oscillator (TCXO). This TCXO is also the reference for the Out Door Unit (ODU). Using the same TCXO for both the counter and the ODU reduces terminal design cost.
FIG. 1 illustrates a block diagram of the related art time and frequency adjustment system. The basic related art method of synchronization is to lock the LMC to the received PCR value from a demodulator 1, using a Phase Locked Loop (PLL) implementation. This related art implementation locks the TCXO to the source at the hub in frequency, and locks the LMC to the PCR. Thus, the terminal is locked in time and frequency to the hub. The received PCR value experiences a random jitter due to the delay in the decoder/demodulator, on the order of plus or minus 2 bytes.
In operation an input signal Rx is received at the demodulator 1, which generates three outputs based on the input signal Rx. The first demodulator output (not illustrated) is the demodulated data, which is the primary output of the modulator, but is not of further interest to the present invention. The second demodulator output is the PCR timestamp shown in FIG. 1. The third demodulator output is a data symbol timing indicator, often implemented as a timing error signal, as discussed below.
In each of the terminals, a control filter 3 receives the PCR timestamp as adjusted by an adder 2 based on the value at the LMC. An output of the control filter 3 is then fed to an oscillator 4, the output of which is fed back into the demodulator 1 and to a counter 5.The output of the counter is the LMC value, and as noted above, is fed back to the adder 2.
This related art scheme has various problems and disadvantages. For example, but not by way of limitation, the stability of the TCXO 4 is affected by at least two phenomena. First, the stability of the TCXO 4 depends on its own phase noise spectrum, as discussed in J. J. Spilker, Digital Communications by Satellite, Prentice-Hall, Inc., Englewood Cliffs, N.J.
Second, the jitter in the received PCR values affects TCXO stability, since adjustments are made to the TCXO 4 periodically based on the PCR values. The phase noise mask of the TCXO 4 in the terminal should be such that the free-running TCXO has a stable output frequency for a time period of at least the time constant of the PLL. Otherwise, the TCXO 4 will change its frequency during the time that it is being adjusted by the loop, and frequency synchronization with the hub will not be accurate.
A total stability of around 10−8, which translates to a frequency error of 140 Hz at Ku band, is acceptable, because this frequency offset can be accommodated by the receiver at the hub. The performance of the loop in the presence of decoder delay has been analyzed, as discussed in greater detail below. To achieve the aforementioned frequency stability, with a decoder/demodulator jitter of plus or minus 2 bytes, and an outbound TDM transmission rate of 5 Msym/sec, the normal frequency of the second order loop should be around 0.001 Hz, assuming a damping of 0.7. The loop settling time for a normal frequency of 0.001 Hz is on the order of 1000 seconds. As a result, the TCXO used at the terminal must have a phase noise mask such that its output frequency, when free-running, is stable for about 1000 seconds. To meet this requirement, an expensive TCXO is required. Thus, there is a cost disadvantage to the TCXO of the related art system.
More specifically, the PCR stream is generated by a stable (i.e., GPS receiver-controlled) 27 MHz clock at the hub, and it is transmitted once every 100 milliseconds on the TDM stream. It is assumed that the TCXO at the terminal is also 27 MHz. Because the system is discrete and linear, work is performed in terms of the z-transform of all the variables. H(z) is the z-transform of the digital filter. The digital filter is such that the entire configuration is equivalent to a second order digital PLL. H(z) can be mathematically represented as:
                              H          ⁡                      (            z            )                          =                                            G              ~                        1                    +                                                                      G                  ~                                2                                            1                -                                  z                                      -                    1                                                                        .                                              (        1        )            The constants {tilde over (G)}1 and {tilde over (G)}2 depend on the sampling frequency, the TCXO gain, the normal frequency and the damping required. The method for deriving {tilde over (G)}1 and {tilde over (G)}2 can be found in Reference 1.
It is also necessary to determine the stability of the frequency of the TCXO, represented by:
                                          standard            ⁢                                                  ⁢            deviation            ⁢                                                  ⁢                          (                              f                k                            )                                            PCR            ⁢                                                  ⁢            clock            ⁢                                                  ⁢            frequency                          .                            (        2        )            
The combined gain of the D/A converter and the counter, denoted by Kv, can be calculated as:
                                          K            v                    =                                                    Δ                ⁢                                                                  ⁢                f                                            2                b                                      ⁢            T                          ,                            (        3        )            where b is the number of bits in the D/A, and Δf is the dynamic range of the TCXO.
The theoretical performance analysis of the related art scheme is discussed below. The expressions for the steady state variance of the TCXO and the time required for the transient error to die to a prescribed level are given. It can be shown using standard linear analysis that:
                                          F            ⁡                          (              z              )                                =                                    Q              ⁡                              (                z                )                                      ⁢                          (                                                P                  ⁡                                      (                    z                    )                                                  +                                  J                  ⁡                                      (                    z                    )                                                              )                                      ,                                  ⁢                              Q            ⁡                          (              z              )                                =                                                    K                v                            T                        ⁢                                                                                (                                          z                      -                      1                                        )                                    ⁢                                      H                    ⁡                                          (                      z                      )                                                                                        z                  -                  1                  +                                                            K                      v                                        ⁢                                          H                      ⁡                                              (                        z                        )                                                                                                        .                                                          (        4        )            
The main concern in this case is the effect of PCR jitter (i.e., the second component J(z)Q(z) in equation (4)), on the adjusted TCXO. The variance of the PCR jitter is denoted by σ2. The jitter in the adjusted TCXO frequency can be calculated mathematically if the PCR jitter is assumed to be Gaussian, as shown below:
                                          σ            f            2                    =                                    1                              2                ⁢                                                                  ⁢                π                ⁢                                                                  ⁢                j                                      ⁢                          σ              2                        ⁢                                          ∮                                                      |                    z                    |                                    =                  1                                            ⁢                                                Q                  ⁡                                      (                    z                    )                                                  ⁢                                  Q                  ⁡                                      (                                          z                                              -                        1                                                              )                                                  ⁢                                  ⅆ                  z                                                                    ,                            (        5        )            
The integral in the above equation has been tabulated for various kinds of rational polynomials. Expanding Q(z) and using the tabulated integrals results in the following:
                                          σ            f            2                    =                                                    σ                2                                            T                2                                      ⁢            2            ⁢                                                            G                  2                                ⁡                                  (                                                            2                      ⁢                                              G                        1                        3                                                              +                                          3                      ⁢                                              G                        1                        2                                            ⁢                                              G                        2                                                              +                                          G                      2                      2                                        +                                                                  G                        1                                            ⁢                                              G                        2                        2                                                                              )                                                                              G                  1                                ⁢                                                      G                    2                                    ⁡                                      (                                          4                      -                                              2                        ⁢                                                  G                          1                                                                    -                                              G                        2                                                              )                                                                                      ,                            (        6        )            where G1 and G2 are Kv{tilde over (G)}1 and Kv{tilde over (G)}2 respectively.
The transient error at the output of the TCXO is similarly derived using linear analysis. The time necessary for the transient error to be less than x Hz is approximated as follows:
                    t        =                                            -              1                                      ζ              ⁢                                                          ⁢              2              ⁢                                                          ⁢              π              ⁢                                                          ⁢                              f                n                                              ⁢                      log            ⁡                          (                                                x                                      f                    e                                                  ⁢                                                      1                    -                                          ζ                      2                                                                                  )                                ⁢                                          ⁢          seconds                                    (        7        )            where fe is the initial error at the TCXO. For a TCXO with 1 ppm accuracy, fe will be at most ±27 Hz. An error of xHz at the 27 MHz clock translated to an error of (14000/27)*xHz at Ku-band. The simulation results of the foregoing theoretical discussion are discussed below. Table 1 shows the expected TCXO clock stability with Gaussian jitter and the comparison with simulations. For purposes of comparison, the variance of the Gaussian jitter was set equal to the uniform jitter. The outbound rate was set to the worst case value of 5 Msym/sec. The D/A resolution was 12 bits and the dynamic range of the TCXO was ±256 Hz. As shown in Table 1, the simulations matched the theoretical predictions. Although the average stability for the uniform and Gaussian jitters are substantially the same, Gaussian jitter can produce much higher errors than uniform jitter. The steady state distribution of frequency error at Ku-band, with uniform jitter, is shown in FIG. 2, which is the offset between the channels and also represents the operating environment of the present invention.
TABLE 1Steady state TCXO stability,2 bytes jitter, fn = 0.001 Hz, damping ratio = 0.707PCR jitterstandardTheoreticalStability withDelaydeviation (in 27stabilityequivalentStability(±bytes)MHz symbols)(Gaussian jitter)(Gaussian jitter)actual jitter135.11.16 × 10−81.16 × 10−81.16 × 10−8260.82.00 × 10−82.00 × 10−82.00 × 10−8
Thus, in the related art, PCR loop bandwidths of about 0.001 Hz are required to achieve low Ku-band frequency errors (less than 500 Hz). However, such a low bandwidth requires about 25 minutes for the transient error at Ku-band to decrease to about 30 Hz.
Another related art solution uses higher loop-bandwidths at startup and switch to lower loop-bandwidths later. However, this related art hub must to tolerate a larger frequency error during startup.